1. Field of the Invention
The present invention relates generally to spacecraft and more particularly to spacecraft stationkeeping.
2. Description of the Related Art
FIG. 1 shows a spacecraft 20 orbiting the Earth 22 in an orbital plane 24. A typical spacecraft includes a body 25, solar cell arrays 26 which are directed towards the Sun for generation of electrical power and at least one antenna 28 which is directed towards the Earth 22 for communication and tracking.
Spacecraft are placed in Earth orbits for a variety of purposes, e.g., weather monitoring, scientific observations and commercial communications. Accordingly, they are maintained in a variety of attitudes and placed in a variety of orbits (e.g., low Earth orbit, transfer orbit, inclined synchronous orbit and geostationary orbit). A spacecraft's attitude is typically defined with respect to a coordinate system that has an origin at the satellite's center of mass. The coordinate system of FIG. 1 has a yaw axis 30 which is directed from the origin towards the Earth's center of mass. A pitch axis 31 is directed from the origin and is normal to the satellite's orbital plane 24. A roll axis 32 is normal to the other two axes and is aligned with the satellite's velocity vector.
A spacecraft's orbital position is typically defined by the orbit's eccentricity, the inclination of the orbital plane from the Earth's equatorial plane and the spacecraft's longitude. In a geostationary orbit, the spacecraft's orbital period matches the Earth's rotational period, the eccentricity is substantially zero and the spacecraft's orbital plane is substantially coplanar with the Earth's equatorial plane. The principal forces which disturb a spacecraft's position are generated by the gravity of the sun and the moon, the Earth's elliptical shape (triaxiality) and solar radiation pressure.
The processes of maintaining a spacecraft's position with respect to the Earth and its attitude with respect to a coordinate system are respectively referred to as stationkeeping and attitude control. Stationkeeping may be facilitated with thrusters which are directed to generate forces through the spacecraft's center of mass. Attitude control is generally facilitated with momentum and/or reaction wheels whose momentum is periodically "dumped" when the same (or different) thrusters are directed to generate turning moments about the spacecraft's center of mass.
Conventional thruster systems typically have sets of thrusters that are aligned in north-south and east-west directions. The north-south thrusters produce north-south velocity changes (.DELTA.V) to control inclination. The east-west thrusters produce an east-west .DELTA.V to control drift (change of longitude with time) and eccentricity.
A different thruster system was described in U.S. Pat. No. 5,443,231 which issued Aug. 22, 1995 to Bernard Anzel and was assigned to Hughes Electronics, the assignee of the present invention. As shown in FIGS. 2A-2C, this thruster system 40 is carried adjacent to an antinadir face 41 of the spacecraft and has thrusters 42, 44, 46 and 48 which are respectively positioned in northwest, northeast, southwest and southeast regions of the antinadir face 41 and directed through the spacecraft's center of mass 50.
When viewed from an east body face 52, the north thrusters 42 and 44 and the south thrusters 46 and 48 are seen to be canted oppositely from the pitch axis 31 by an angle .theta.. When viewed from a north body face 54, the west thrusters 42 and 46 and east thrusters 44 and 48 are oppositely slewed from the yaw axis 30 by an angle .alpha.. These angles can be changed as required, e.g., with gimbals and servo mechanisms.
In an exemplary stationkeeping process, the north thrusters 42 and 44 and the south thrusters 46 and 48 are respectively fired in the regions of 90 degrees R.A. (right ascension) and 270 degrees R.A. so that their normal thrust components (normal to the orbital plane) control inclination errors. The radial thrust components of the north and south thrusters are opposed in direction and, if not equal, may generate a net eccentricity component. However, since these radial thrust components are directed inward, they produce an unwanted eastward longitudinal shift which can be compensated with tangential thrust components.
The north and south thrusters can generate a net tangential thrust component that adjusts eccentricity along an axis through 90 degrees R.A. and 270 degrees R.A.. This tangential thrust component also changes the orbital diameter to counter the drift effects of the triaxiality force (a tangential force caused by the Earth's triaxiality and whose magnitude and direction are a function of the spacecraft's longitudinal position) and the unwanted eastward longitudinal drift mentioned above. The north and south thrusters can also generate a net radial thrust component that controls orbital eccentricity along an axis through 0 degrees R.A. and 180 degrees R.A.
Geostationary spacecraft must typically be stationkept within assigned orbital "boxes" which have predetermined side dimensions (e.g., .about.147 kilometers). Because the number of geostationary boxes is limited and communication demands constantly increase, there is increasing commercial pressure to locate more than one satellite in an orbital box, i.e., an increasing pressure to co-locate n satellites in a single orbital box. Accordingly, in copending application Ser. No. 08/701,513, filed Aug. 22, 1996 in the name of Bernard Anzel and assigned to Hughes Electronics, the assignee of the present invention, the thruster system 40 of FIGS. 2A-2C is used in a novel co-location method.
Stationkeeping of spacecraft in geostationary orbits necessarily includes reduction of orbital inclination. Of the orbital parameters (i.e., inclination, eccentricity and drift), control of inclination requires the most thruster fuel. However, inclination control is generally not needed for spacecraft in inclined orbits. Stationkeeping and momentum dumping for such spacecraft will thus typically require control processes that differ from those which are suited for spacecraft in geostationary orbits.